学术探索
学术期刊
新闻热点
数据分析
智能评审

A survey of credibility theory

被引：65
作者：
Liu B. [1 ]
机构：
[1] Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University
来源：
Fuzzy Optimization and Decision Making | 2006年 / 5卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Conditional credibility; Credibility measure; Credibility theory; Fuzzy random variable; Fuzzy variable; Random fuzzy variable;
D O I：
10.1007/s10700-006-0016-x
中图分类号：
学科分类号：
摘要：
This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented. © Springer Science+Business Media, LLC 2006.
引用
收藏
页码：387 / 408
页数：21
相关论文
共 105 条
  • [61] Liu Y.K., Gao J., Convergence criteria and convergence relations for sequences of fuzzy random variables, Lecture Notes in Artificial Intelligence, 3613, pp. 321-331, (2005)
  • [62] Loo S.G., Measures of fuzziness, Cybernetica, 20, pp. 201-210, (1977)
  • [63] Lu M., Gao J., Fuzzy expected value integer programming models for capital budgeting problem, Proceedings of the Fourth National Youth Conference on Operations Research and Management, pp. 242-249, (2001)
  • [64] Nahmias S., Fuzzy variables, Fuzzy Sets and Systems, 1, pp. 97-110, (1978)
  • [65] Pal N.R., Pal S.K., Higher order fuzzy entropy and hybrid entropy of a set, Information Sciences, 61, pp. 211-231, (1992)
  • [66] Peng J., Liu B., Parallel machine scheduling models with fuzzy processing times, Information Sciences, 166, 1-4, pp. 49-66, (2004)
  • [67] Peng J., Liu B., Some properties of optimistic and pessimistic values of fuzzy variables, Proceedings of the Thirteenth IEEE International Conference on Fuzzy Systems, 2, pp. 745-750, (2004)
  • [68] Peng J., Mok H.M.K., Tse W.M., Fuzzy dominance based on credibility distributions, Lecture Notes in Artificial Intelligent, 3613, pp. 295-303, (2005)
  • [69] Peng J., Mok H.M.K., Tse W.M., Credibility programming approach to fuzzy portfolio selection problems, Proceedings of 2005 International Conference on Machine Learning and Cybernetics., 4, pp. 2523-2528, (2005)
  • [70] Puri M.L., Ralescu D.A., Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, pp. 409-422, (1986)
234567891011